No, you don’t. If I also have a laptop and my water bottle in my hands - which is always the case plus I might have food in my hand as well - I don’t have the dexterity to text. And not every text makes sense to reply to “busy ttyl”. If I get a text that requires a real reply, I’m not sending an extra empty “busy” reply. Furthermore as a grown ass person juggling multiple things, having multiple thoughts, it’s easy to get out a meeting, the gym, etc and forget about the text you read an hour ago until later in the day when you’re fukking with your phone or get another messsage.
Bruh, I don’t know where you are with this chick, but you said you’re dating a lot of people and have other women that reply faster, this denotes she’s one of many, which women can sense and they deal with you accordingly. Her not texting to confirm the time is annoying, yes, but other general chit chat texts, a delay is reasonable. Have y’all gone out, how was she? Has she hung out other times you’ve set things up? If so, stop tripping, she’s clearly somewhat interested. She said she was out, to be honest she either was just having too much fun with the friends she was out with or met some dude for the night and whipping out a phone during their convo to text you wasn’t taking precedent. In any case, until y’all are serious, you don’t warrant her changing her communication style at the moment.
That passive aggressive text you sent about how booked up your are all week was wack too. Definitely could have let her know you made other plans today, made a joke about how she was too slow and just jumped to trying to set something up on Thursday, not slide in how you’re booked every other day that week too. But yea, do you. If this is a deal breaker, then stop dealing with her, otherwise you just sound hurt that she’s not feeling you the same (just yet...never know, it might change)